Central Tendency: Mean, Median and Mode
Nisha asks a simple question: "How many cold coffees do we sell on a typical day?" There are three honest answers for the same week, and they are not the same number. Knowing which one to give, and why they differ, is the first skill of describing any column.
| day | Mon | Tue | Wed | Thu | Fri | Sat | Sun |
|---|---|---|---|---|---|---|---|
| cups | 40 | 38 | 36 | 43 | 46 | 95 | 38 |
The rule
Mean shares it out, median stands in the middle, mode shows up most.
- Mean: add everything and share it equally. 336 ÷ 7 = 48. Every value pulls on it, including the extreme ones.
- Median: sort, then take the middle value. Sorted: 36, 38, 38, 40, 43, 46, 95, so the median is 40. With an even number of values, average the middle two.
- Mode: the most frequent value. 38 appears twice, so the mode is 38. A column can have no mode, or several.
Which to use depends on the data:
| situation | best measure |
|---|---|
| roughly symmetric, no extremes | mean |
| skewed, or has outliers (incomes, delivery times, this week) | median |
| categories (most popular item, busiest weekday) | mode |
| you need a total later (stock for the week) | mean, since mean × count = total |
Here six of seven days sold 46 or fewer, yet the mean is 48. One fair Saturday pulled it up. The median, 40, describes a typical day far better. In a spreadsheet: =AVERAGE(...), =MEDIAN(...), =MODE.SNGL(...).
The shortcut
Compare the mean and the median. If they are close, the data is balanced and either works. If the mean is well above the median, something large is pulling it; report the median as "typical".
Mean
Total 336, seven days: 336 ÷ 7 = 48.
The trap: the mean of a skewed column describes almost no one. "Average delivery time is 50 minutes" can be true while most deliveries take 30.
Drills
Answer fast — trust the rule.
What is the mean of the five weekdays, Monday to Friday (40, 38, 36, 43, 46)?
What is the median of 40, 38, 36, 43, 46, 38 (the week without Saturday)?
Which is the best measure for "the most popular item on the menu"?
Adding Saturday's 95 changes which measure the most?
A day's sales for a whole year have mean 52 and median 44. What does this suggest?
Remember
- Mean shares it out, median stands in the middle, mode shows up most.
- Shortcut: mean well above median means something big is pulling; report the median as typical.
- Trap: the mean of a skewed column describes almost nobody.